arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2012.02303math.OCcs.MAmath.DSmath.PR
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去中心化状态依赖马尔可夫链综合及其在群体引导中的应用

Decentralized State-Dependent Markov Chain Synthesis with an Application to Swarm Guidance

Samet Uzun, Nazim Kemal Ure, Behcet Acikmese

AI总结:

本文提出去中心化状态依赖马尔可夫链综合(DSMC)算法,基于状态依赖共识协议实现指数收敛,并在概率群体引导仿真中验证了比已有算法更快的收敛速度。

摘要:

本文针对有限状态马尔可夫链,提出了一种去中心化状态依赖马尔可夫链综合(DSMC)算法。我们提出了一种状态依赖共识协议,该协议在温和的技术条件下实现了指数收敛,且不依赖于关于动态网络拓扑的任何连通性假设。利用所提出的共识协议,我们开发了DSMC算法,该算法基于当前状态更新马尔可夫矩阵,同时确保共识协议的收敛条件。该结果为生成的马尔可夫链确立了所需的稳态分布,确保从所有初始分布呈指数收敛,同时遵守转移约束并最小化状态转移。DSMC的性能通过一个概率群体引导示例得到展示,该示例将包含大量移动代理的群体的空间分布解释为概率分布,并利用马尔可夫链计算状态之间的转移概率。仿真结果表明,与先前基于马尔可夫链的群体引导算法相比,基于DSMC的算法具有更快的收敛速度。

英文摘要:

This paper introduces a decentralized state-dependent Markov chain synthesis (DSMC) algorithm for finite-state Markov chains. We present a state-dependent consensus protocol that achieves exponential convergence under mild technical conditions, without relying on any connectivity assumptions regarding the dynamic network topology. Utilizing the proposed consensus protocol, we develop the DSMC algorithm, updating the Markov matrix based on the current state while ensuring the convergence conditions of the consensus protocol. This result establishes the desired steady-state distribution for the resulting Markov chain, ensuring exponential convergence from all initial distributions while adhering to transition constraints and minimizing state transitions. The DSMC's performance is demonstrated through a probabilistic swarm guidance example, which interprets the spatial distribution of a swarm comprising a large number of mobile agents as a probability distribution and utilizes the Markov chain to compute transition probabilities between states. Simulation results demonstrate faster convergence for the DSMC based algorithm when compared to the previous Markov chain based swarm guidance algorithms.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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